Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood211 Estimation

摘要

Sparse coding is a method for finding a representation of data in which each of211u001ethe components of the representation is only rarely significantly active. Such a 211u001erepresentation is closely related to redundancy reduction and independent 211u001ecomponent analysis, and has some neurophysiological plausibility. In this paper, 211u001ethe authors show how sparse coding can be used for denoising. Using maximum 211u001elikelihood estimation of nongaussian variables corrupted by gaussian noise, the 211u001eauthors show how to apply a soft-thresholding (shrinkage) operator on the 211u001ecomponents of sparse coding so as to reduce noise. The authors' method is closely 211u001erelated to the method of wavelet shrinkage, but it has the important benefit over 211u001ewavelet methods that the representation is determined solely by the statistical 211u001eproperties of the data. The wavelet representation, on the other hand, relies 211u001eheavily on certain mathematical properties (like self-similarity) that may be 211u001eonly weakly related to the properties of nautral data.